10th Class Mathematics Surface Areas and Volumes Question Bank Surface Area and Volume (Mensuration)

  • question_answer A circular tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

    A)  3894 m                       

    B)  973.5 m       

    C)  1947 m   

    D)  1800 m

    Correct Answer: C

    Solution :

    (c): Radius = 52.5 m Area of the entire canvas, used for the tent = Surface area of cylinder + Surface area of cone \[=2\pi rh+\pi rl\] \[=2\times \frac{22}{7}\times 52.5\times 3+\frac{22}{7}\times 52.5\times 53\] This surface areas has to be equal to \[5\times \ell \] where \[\ell =\] length of canvas. Thus, we have \[5\ell =2\times \frac{22}{7}\times 52.5\times 3+\frac{22}{7}\times 52.5\times 53\] \[\Rightarrow \]   \[\ell =1947\,\,m\]          

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